An approximate solution of a weighted scheduling problem with multiple constraints

The general problem of scheduling n items in some optimal fashion has been of interest for many years. Several variations of this problem are frequently encountered in industry. A recent example, the scheduling of manned space experiments, requires a scheme for selection and scheduling of n experiments in a fixed mission time. Since the number of experiments performed on a given flight may be large, the total number of possible schedules could be enormous. Hence, the practicality of a direct approach, even using the fastest digital computers available, is questionable.

In order to attack this problem a technique was developed which provides a solution “optimal” in the following sense: If points are assigned to each experiment, then the optimal solution is that schedule in which the total number of points is greatest. The technique schedules one experiment at a time, but not necessarily sequentially in mission time. Instead, it schedules experiments in those time slots which yield an immediate approximation to an optimal schedule. The problem of optimal scheduling of n items in this sense is well known. As far as we know, no unique computational algorithm exists for the problem. In fact, no general theory has been developed which is applicable to this problem. The technique presented here is offered as a feasible computer solution.